I have attached the files. Question 1 & 3 need done. Thanks

Business Finance 4223 Assignment #1 Treasury Bonds and Trades Due in class on February 2, 2016 The focus of this assignment is to understand how to construct portfolios of Treasuries and to hedge interest rate risk. You will need to use a spreadsheet posted on Carmen called hw1data.xls. You can work in a group of 1 - 4 people. Each group should hand in one copy of their answers. Show your work and provide explanations where relevant. However, you do not need to print out entire spreadsheets. Your answers should be summarized in a write-up with relevant details of calculations, tables and charts (if applicable), and explanations. Question 1: Trading on the Level of Interest Rates Suppose that you are given the following zero-curve (interest rates are annual, but compounded semi-annually): t r 0.5 1 1.5 2 2.5 3 3.5 4 0.02 0.021 0.023 0.025 0.03 0.035 0.04 0.041 1. Calculate the value of a 4-year Treasury bond with a 10% coupon rate, coupons paid semi-annually, and a face value of $100. 2. Calculate the modied duration and convexity of the bond in (1). You can use the approximation formulas from class. What is the approximate percentage change in the bond price if the zero-curve shifts up by one percentage point (i.e. r0.5 = 0.03, r1 = 0.031, etc.)? 3. Because you believe that the zero-curve will shift upward and decrease the bond price, you decide to use a reverse repo trade to short the bond. Let's suppose that a repo dealer quotes you a special repo rate of 2% and you borrow 100 units of the Treasury bond (which you then sell on the market as part of your reverse repo transaction). (a) Draw a picture of the initial transactions in the repo trade. (b) If the zero-curve shifts up by one percentage point, what is the value of the Treasury bond in part 1? (c) What is your net payo to unwinding the repo trade tomorrow? Recall that you need to buy the bond and sell it to the repo dealer at the prespecied price. Assume that the price tomorrow is the price that you calculated in (b). Question 2: Steepener Trade For this part, use the Fama-Bliss tab in hw1data.xls. This le contains zero-coupon yields (reported in %). For simplicity, assume that the yields are annually compounded. 1 1. It is November 30, 2010 and you hold a $1mm (market value) long position in the 1-yr zero-coupon bond. Using modied durations, determine how much of the 5-yr zerocoupon bond you need to short so that your portfolio remains approximately unchanged if the 1-yr and 5-yr zero rates move in parallel. This is known as a steepener trade - you prot if the yield curve becomes steeper. What is the market value of your portfolio? 2. What actually happens during the following month? Calculate the value of your portfolio. A 1-yr bond is now an 11-month bond and a 5-yr bond becomes a 4-year 11-month bond. Assume for pricing purposes that the 5-yr rate applies to the 4-yr 11-month bond and the 1-yr rate applies to an 11-month bond when calculating bond prices. Why did your portfolio value change from before? 3. What would the change in your portfolio value have been if the 1-yr rate had stayed the same and the 5-yr rate had gone down by 0.5 percentage points? Question 3: Buttery Strategy One of the more popular strategies in the Fixed Income market is the Buttery Strategy which constructs a trade that is protable if the term structure of interest rates moves in parallel. In this problem, you will be asked to construct the right portfolio weights for this trade and to determine the protability of the trade. Start with the following table of zero-coupon bonds: Maturity Yield 2 years 5% 5 years 5% 10 years 5% The strategy is based on buying the 2-year and 10-year bonds and shorting the 5-year bond. It will end up having a positive convexity. The relative amounts to invest in each bond are given by the two constraints: (1) It should be (modied) duration neutral. That is, construct the strategy such that the dollar value of your short position times the modied duration of your short position is equal to the dollar value of your long position times the modied duration of your long position. Thus, it is hedged against small (level) changes in yields. (This is the constraint from a number of the examples given in class.) (2) It should be \"cash neutral\". That is, the initial value of the short position should equal the initial value of the long position. 1. Calculate the modied duration of the 2-year, 5-year, and 10-year bonds. 2. Suppose you short $1,000 in face value of the 5-year bond. First, calculate the market value of the 5-year bond. Denote x to be the amount (market value) of the 2-year bond that you buy and z the amount (market value) of the 10-year bond you buy. Write down the two equations for the two constraints given above. 2 3. Solve the two equations for x and z. These are the market values of the 2-year and 10-year bonds that you buy in this strategy. What is the face value of the 2-year and 10-year bonds that you buy? 4. Suppose that yields move in parallel to 4.75%. What is the prot/loss to your strategy? What about 4.5%? Do this calculation for each 0.25% increment from a yield of 0% to a yield of 10% and plot the prot/loss against the yield. 5. Suppose that instead, the yields move to y2 = 3%, y5 = 5%, and y10 = 8%. What is the prot/loss of your position? 3